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Contemporary Mathematics. Fundamental Directions, 2021, Volume 67, Issue 4, Pages 668–692
DOI: https://doi.org/10.22363/2413-3639-2021-67-4-668-692 (Mi cmfd442) 		 
Weierstrass polynomials in estimates of oscillatory integrals

I. A. Ikromov, A. S. Sadullaev

Samarkand State University named after A. Navoi, Samarkand, Uzekistan
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DOI: https://doi.org/10.22363/2413-3639-2021-67-4-668-692
Abstract: In this paper, estimates are obtained for the Fourier transform of smooth charges (measures) concentrated on some nonconvex hypersurfaces. The summability of the maximal Randall function is proved for a wide class of nonconvex hypersurfaces. In addition, in the three-dimensional case, estimates are obtained depending on the Varchenko height. The accuracy of the obtained estimates is proved. The proof of the estimate for oscillatory integrals is based on the Weierstrass preparatory theorem.
Funding agency Grant number
Academy of Sciences of the Republic of Uzbekistan ОТ-Ф-4-69
ОТ-Ф-4-37/29
Document Type: Article
UDC: 517.518
Language: Russian
Citation: I. A. Ikromov, A. S. Sadullaev, “Weierstrass polynomials in estimates of oscillatory integrals”, Science — Technology — Education — Mathematics — Medicine, CMFD, 67, no. 4, PFUR, M., 2021, 668–692
Citation in format AMSBIB
\Bibitem{IkrSad21}
\by I.~A.~Ikromov, A.~S.~Sadullaev
\paper Weierstrass polynomials in estimates of oscillatory integrals
\inbook Science — Technology — Education — Mathematics — Medicine
\serial CMFD
\yr 2021
\vol 67
\issue 4
\pages 668--692
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd442}
\crossref{https://doi.org/10.22363/2413-3639-2021-67-4-668-692}
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